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Generalized fractional smoothness and Lp-variation of BSDEs with non-Lipschitz terminal condition

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  • Geiss, Christel
  • Geiss, Stefan
  • Gobet, Emmanuel
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    Abstract

    We relate the Lp-variation, 2≤p<∞, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness takes into account the quantitative propagation of singularities in time.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 5 ()
    Pages: 2078-2116

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:5:p:2078-2116

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    Related research

    Keywords: Backward stochastic differential equation; Lp-variation; Fractional smoothness; Besov spaces;

    References

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    1. Hu, Ying & Ma, JinJin, 2004. "Nonlinear Feynman-Kac formula and discrete-functional-type BSDEs with continuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 112(1), pages 23-51, July.
    2. Rainer Avikainen, 2009. "On irregular functionals of SDEs and the Euler scheme," Finance and Stochastics, Springer, vol. 13(3), pages 381-401, September.
    3. Emmanuel Temam & Emmanuel Gobet, 2001. "Discrete time hedging errors for options with irregular payoffs," Finance and Stochastics, Springer, vol. 5(3), pages 357-367.
    4. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    5. Briand, Ph. & Delyon, B. & Hu, Y. & Pardoux, E. & Stoica, L., 2003. "Lp solutions of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 109-129, November.
    6. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, June.
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